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Monotone matrix functions of successive orders

Nayak, Suhas (2004) Monotone matrix functions of successive orders. Proceedings of the American Mathematical Society, 132 (1). pp. 33-35. ISSN 0002-9939.

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This paper extends a result obtained by Wigner and von Neumann. We prove that a non-constant real-valued function, f(x), in C^3(I) where I is an interval of the real line, is a monotone matrix function of order n+1 on I if and only if a related, modified function gx0 (x) is a monotone matrix function of order n for every value of x0 in I, assuming that f' is strictly positive on I.

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Additional Information:©2003 American Mathematical Society. Received by the editors August 25, 2002. Article electronically published on July 17, 2003. This work was conducted as part of a senior thesis at the California Institute of Technology. The author wishes to thank B. Simon for uncovering the Wigner and von Neumann continued fraction proof and the paper on which this research is based, and for many helpful discussions.
Subject Keywords:monotone matrix functions; Löwner's Theorem; Sylvester's Determinant Identity
Issue or Number:1
Record Number:CaltechAUTHORS:NAYpams04
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10651
Deposited By: Tony Diaz
Deposited On:02 Jun 2008
Last Modified:03 Oct 2019 00:11

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